But if Dave Walker had his druthers, Republicans would switch to a “semi-open” primary to allow the state’s largest electorate bloc, unaffiliated voters, to cast votes for the party’s candidates.

The gubernatorial hopeful and former U.S. comptroller general, who resides in Bridgeport, said there’s a legitimate upside to changing the eligibility rules of the GOP’s closed primary system.

“Republicans represent 21 percent of the voting base,” Walker said. “I think it could help us broaden our appeal and better position us for general election victories.”

Connecticut’s GOP briefly allowed unaffiliated voters to participate in its primaries in the mid-1980s, but reverted to a closed system when John Rowland was governor. Nineteen states have some form of open primaries.

To change the party’s bylaws, it would require the approval of the Republican State Central Committee and delegates at the state party’s nominating convention in May, which Walker acknowledged won’t happen this year. Walker was a member of a state GOP task force that examined the issue, but took no action.

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The subject of open versus closed primaries, or some hybrid, has long been a contentious one in GOP — and now is no different.

Tim Herbst, a bitter adversary of Walker in the governor’s race and former Trumbull first selectman, staunchly opposes opening up the primary to anyone and said that checks and balances for party switches aren’t foolproof.

“What could happen is Democrats could infiltrate an open primary process to nominate a candidate they felt was more beatable,” Herbst said.

He took Walker and fellow GOP gubernatorial contender Mark Boughton, Danbury’s mayor, to task over their current and past support for allowing unaffiliated voters to cast primary ballots. In a 2014 op-ed piece for the Hartford Courant, Boughton advocated for the change. Herbst noted that Walker finished third that year in the GOP lieutenant governor primary and that Boughton suspended his campaign before the primary.

“I find it very interesting that both Mr. Walker and Mr. Boughton after both lost a nominating contest and a primary sometimes take their toys and go home and rewrite the rules to suit them,” Herbst said.

Boughton said he no longer supports a semi-open primary, however.

“I kind of changed my thinking on that a little bit,” Boughton said, adding that the large GOP field for governor shows the energy in the party. “The Connecticut Republican Party is alive and well.”